Differential polynomial equation systems.

GABRIELA JERONIMO

Angra dos Reis, Brasil

Workshop; Second Latin American Workshop on Polynomial Systems; 2005

We consider a class of ordinary first order multivariate polynomial differential systems related to the observability problem from control theory and investigate the application of algebraic and geometric tools to their resolution. Given a polynomial differential system, we focus on the computation of the differential Hilbert function of the prime differential ideal associated with the system and of a transcendence basis of the induced differential field extension, a starting point towards the computation of a resolvent representation of the ideal. First, we establish theoretical formulae for the differential Hilbert function and we design a probabilistic algorithm for its computation. Then, we show an algebraic criterion for deciding differential transcendence which is the basis for the algorithm solving the second task. (Joint work with Lisi D'Alfonso and Pablo Solernó.)